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[Перевод] Как работают трансформеры: разбираем математику

fc1a4c81f273b8ed87c1861e5aa8c210.png

В этом посте я представлю подробный пример математики, используемой внутри модели трансформера, чтобы вы получили хорошее представление о работе модели. Чтобы пост был понятным, я многое упрощу. Мы будем выполнять довольно много вычислений вручную, поэтому снизим размерность модели. Например, вместо эмбеддингов из 512 значений мы используем эмбеддинги из 4 значений. Это позволит упростить понимание вычислений. Мы используем произвольные векторы и матрицы, но при желании вы можете выбрать собственные значения.

Как вы увидите, математика модели не так уж сложна. Сложность возникает из-за количества этапов и количества параметров. Перед прочтением этой статьи я рекомендую прочитать пост Illustrated Transformer (или читать их параллельно) [перевод на Хабре]. Это отличный пост, объясняющий модель трансформера интуитивным (и наглядным!) образом, поэтому я не буду объяснять то, что уже объяснено в нём. Моя цель заключается в том, чтобы объяснить, как работает модель трансформера, а не что это такое. Если вы хотите углубиться в подробности, то изучите известную статью Attention is all you need [перевод на Хабре: первая и вторая части].

Обязательные требования

Для понимания статьи необходимы базовые знания линейной алгебры; в основном мы будем выполнять простые матричные умножения, так что специалистом быть необязательно. Кроме того, будут полезны знания основ машинного обучения и глубокого обучения.

Что рассматривается в статье?

  • Полный пример математических вычислений, происходящих в модели трансформера в процессе инференса

  • Объяснение механизмов внимания

  • Объяснение остаточных связей и нормализации слоёв

  • Код для масштабирования модели

Наша цель будет заключаться в использовании модели трансформера в качестве инструмента для перевода, чтобы мы могли передать модели входные данные и ожидать от неё генерации перевода. Например, мы можем передать «Hello World» на английском и ожидать на выходе получить «Hola Mundo» на испанском.

Давайте взглянем на пугающую диаграмму трансформера (не бойтесь, скоро вы её поймёте!):

Модель трансформера из статьи «Attention is all you need»
Модель трансформера из статьи «Attention is all you need»

Исходная модель трансформера состоит из двух частей: кодировщика (encoder) и декодера (decoder). Кодировщик занимается «пониманием» или «осознанием смысла» входного текста, а декодер выполняет генерацию выходного текста. Давайте рассмотрим кодировщик.

Кодировщик

Цель работы кодировщика заключается в генерации обогащённого эмбеддингами описания входного текста. Этот эмбеддинг отражает семантическую информацию о входном тексте и передаётся декодеру для генерации выходного текста. Кодировщик состоит из стека из N слоёв. Прежде чем переходить к слоям, нужно разобраться, как передавать слова (или токены) в модель.

Примечание

Термин «эмбеддинг» используется слишком часто. Сначала мы создадим эмбеддинг, который будет входными данными для кодировщика. Кодировщик тоже создаёт на выходе эмбеддинг (иногда называемый hidden states). Декодер тоже получает эмбеддинг! Весь смысл в том, что эмбеддинг описывает токен в виде вектора.

0. Токенизация

Модели машинного обучения могут обрабатывать числа, а не текст, так что нам нужно превратить входной текст в числа. Именно это и выполняет токенизация! Это процесс разбиения входного текста на токены, с каждым из которых связан ID. Например, мы можем разделить текст «Hello World» на два токена: «Hello» и «World». Также мы можем разбить его на символы: «H», «e», «l», «l», «o», « »,«W», «o», «r», «l», «d». Мы сами можем выбирать принцип токенизации, он зависит от данных, с которыми мы работаем.

Для токенизации по словам (разбиения текста на слова) требуется очень большой словарь (всех возможных токенов). В нём слова наподобие «dog» и «dogs» или «run» и «running» будут разными токенами. Словарь символов потребует меньшего объёма, но будет обладать меньшим смыслом (он может быть полезен в языках наподобие китайского, где каждый символ содержит больше информации).

Прогресс двинулся в сторону токенизации по подсловам. Это нечто среднее между токенизацией по словам и по символам. Мы разделяем слова на подслова. Например, слово «tokenization» можно разбить на «token» и «ization». Как принимается решение о месте разбиения слов? Это часть обучения токенизатора при помощи статистического процесса, задача которого заключается в выявлении подслов, которые лучше всего выбрать для конкретного датасета. Это детерминированный процесс (в отличие от обучения модели машинного обучения).

В этой статье я для простоты использую токенизацию по словам. Наша цель будет заключаться в переводе «Hello World» с английского на испанский. Пример «Hello World» мы разобьём на токены «Hello» и «World». Каждому токену присваивается в словаре модели ID. Например, «Hello» может быть токеном 1, а «World» — токеном 2.

1. Эмбеддинг текста

Хотя мы можем передать модели ID токенов (то есть 1 и 2), эти числа не несут никакого смысла. Нужно превратить их в векторы (список чисел). Именно это и выполняет процесс эмбеддинга! Эмбеддинги токена сопоставляют ID токена с вектором фиксированной длины, имеющим семантическое значение токенов. Это создаёт интересные свойства: схожие токены будут иметь схожий эмбеддинг (иными словами, вычисление косинусного коэффициента между двумя эмбеддингами даст нам хорошее понимание степени схожести токенов).

Стоит заметить, что отображение токена в эмбеддинг изучается моделью. Хотя мы можем использовать уже обученный эмбеддинг наподобие word2vec или GloVe, в процессе своего обучения модели трансформеров изучают эти эмбеддинги. Это большое преимущество, поскольку модель может изучить наилучшее описание токенов для поставленной перед ней задачи. Например, модель может научиться тому, что «dog» и «dogs» должны иметь схожие эмбеддинги.

Все эмбеддинги в одной модели имеют одинаковый размер. В трансформере из научной статьи использовался размер 512, но чтобы мы могли выполнять вычисления, снизим его размер до 4. Я назначу каждому токену случайные значения (как говорилось выше, это отображение обычно изучается моделью).

Hello -> [1,2,3,4]

World -> [2,3,4,5]

Примечание

После публикации статьи многие читатели задали вопросы о представленных выше эмбеддингах. Мне было лениво и я просто записал числа, с которыми будет удобно выполнять вычисления. На практике эти числа будут изучаться моделью. Чтобы это было понятнее, я дополнил пост.

Мы можем вычислить схожесть этих векторов при помощи косинусного коэффициента, который для представленных выше векторов будет слишком высоким. На практике вектор, скорее всего, будет выглядеть примерно так: [-0.071, 0.344, -0.12, 0.026, …, -0.008].

Мы можем представить наши входные данные в виде единой матрицы

21ac942d73e513a75f7e6435f4827fca.png

Примечание

Хотя мы и можем обрабатывать два эмбеддинга как два отдельных вектора, проще работать с ними как с единой матрицей, потому что в дальнейшем мы будем выполнять умножение матриц.

2. Позиционное кодирование

Отдельные эмбеддинги в матрице не содержат информации о позиции слов в предложении, так что нам нужна информация о позиции. Её можно создать, добавив к эмбеддингу позиционное кодирование.

Получить его можно различными способами; мы можем использовать изученный эмбеддинг или фиксированный вектор. В исходной научной статье используется фиксированный вектор, потому что авторы не увидели почти никакой разницы между двумя методиками (см. раздел 3.5 статьи). Мы тоже воспользуемся фиксированным вектором. Функции синуса и косинуса имеют волнообразный паттерн и повторяются. Благодаря использованию этих функций каждая позиция в предложении получает уникальное, но согласованное позиционное кодирование. Их повторяемость поможет модели проще изучать паттерны наподобие близости и расстояния между элементами. В статье используются следующие функции:

07739ac8ce5c811f974ff3d5150159cc.png

Смысл заключается в интерполяции между синусом и косинусом для каждого значения в эмбеддинге (для чётных индексов используется синус, для нечётных используется косинус). Давайте вычислим их для нашего примера!

Для «Hello»

  • i = 0 (чётный): PE(0,0) = sin(0 / 10000^(0 / 4)) = sin(0) = 0

  • i = 1 (нечётный): PE(0,1) = cos(0 / 10000^(2*1 / 4)) = cos(0) = 1

  • i = 2 (чётный): PE(0,2) = sin(0 / 10000^(2*2 / 4)) = sin(0) = 0

  • i = 3 (нечётный): PE(0,3) = cos(0 / 10000^(2*3 / 4)) = cos(0) = 1

Для «World»

  • i = 0 (чётный): PE(1,0) = sin(1 / 10000^(0 / 4)) = sin(1 / 10000^0) = sin(1) ≈ 0.84

  • i = 1 (нечётный): PE(1,1) = cos(1 / 10000^(2*1 / 4)) = cos(1 / 10000^0.5) ≈ cos(0.01) ≈ 0.99

  • i = 2 (чётный): PE(1,2) = sin(1 / 10000^(2*2 / 4)) = sin(1 / 10000^1) ≈ 0

  • i = 3 (нечётный): PE(1,3) = cos(1 / 10000^(2*3 / 4)) = cos(1 / 10000^1.5) ≈ 1

В итоге получаем следующее:

  • «Hello» -> [0, 1, 0, 1]

  • «World» -> [0.84, 0.99, 0, 1]

Обратите внимание, что эти кодировки имеют ту же размерность, что и исходный эмбеддинг.

Примечание

Мы используем синус и косинус, как и в исходной научной статье, но есть и другие способы реализации. В очень популярном трансформере BERT применяются обучаемые позиционные эмбеддинги.

3. Добавляем позиционное кодирование и эмбеддинг

Теперь мы добавим к эмбеддингу позиционное кодирование. Это выполняется сложением двух векторов.

«Hello» = [1,2,3,4] + [0, 1, 0, 1] = [1, 3, 3, 5]

«World» = [2,3,4,5] + [0.84, 0.99, 0, 1] = [2.84, 3.99, 4, 6]

То есть наша новая матрица, которая будет входными данными для кодировщика, выглядит так:

b3c1f5027a551dfb3e3e73cc91d26fa3.png

Если посмотреть на изображение из научной статьи, то можно увидеть, что мы только что выполнили левую нижнюю часть изображения (эмбеддинг + позиционное кодирование).

Модель трансформера из статьи «Attention is all you need»
Модель трансформера из статьи «Attention is all you need»

4. Самовнимание

4.1 Определение матриц

Теперь мы введём концепцию многоголового внимания (multi-head attention). Внимание — это механизм, позволяющий модели сосредоточиться на определённых частях входных данных. Многоголовое внимание позволяет модели совместно уделять внимание информации из различных подпространств описаний. Для этого используются множественные головы внимания. Каждая голова внимания имеет собственные матрицы K, V и Q.

Давайте в нашем примере используем две головы внимания. Для этих матриц мы применим случайные значения. Каждая матрица будет иметь размер 4x3. Благодаря этому каждая матрица будет преобразовывать четырёхмерные эмбеддинги в трёхмерные ключи (K), значения (V) и запросы (Q). Это снижает размерность механизма внимания, что помогает управлять вычислительной сложностью. Стоит отметить, что использование слишком малого размера внимания уменьшит точность модели. Давайте используем следующие значения (выбраны произвольно):

Для первой головы

6d6536a6f378872e5551e5ae957dbdf9.png

Для второй головы

ae855c0cdc319b6b83cbfe04f7b10b73.png

4.2 Вычисление ключей, запросов и значений

Для получения ключей, запросов и значений нужно умножить входные эмбеддинги на матрицы весов.

Вычисление ключей

b022aa1304298a0573f65941cb2d6acf.png

На самом деле, нам не нужно вычислять всё это вручную, это будет слишком монотонно. Давайте схитрим и воспользуемся NumPy.

Сначала определим матрицы

import numpy as np

WK1 = np.array([[1, 0, 1], [0, 1, 0], [1, 0, 1], [0, 1, 0]])
WV1 = np.array([[0, 1, 1], [1, 0, 0], [1, 0, 1], [0, 1, 0]])
WQ1 = np.array([[0, 0, 0], [1, 1, 0], [0, 0, 1], [1, 0, 0]])

WK2 = np.array([[0, 1, 1], [1, 0, 1], [1, 1, 0], [0, 1, 0]])
WV2 = np.array([[1, 0, 0], [0, 1, 1], [0, 0, 1], [1, 0, 0]])
WQ2 = np.array([[1, 0, 1], [0, 1, 0], [1, 0, 0], [0, 1, 1]])

И убедимся, что в приведённых выше вычислениях нет никаких ошибок.

embedding = np.array([[1, 3, 3, 5], [2.84, 3.99, 4, 6]])
K1 = embedding @ WK1
K1
array([[4.  , 8.  , 4.  ],
       [6.84, 9.99, 6.84]])

Отлично! Теперь давайте получим значения и запросы

Вычисление значений

V1 = embedding @ WV1
V1
array([[6.  , 6.  , 4.  ],
       [7.99, 8.84, 6.84]])

Вычисление запросов

Q1 = embedding @ WQ1
Q1
array([[8.  , 3.  , 3.  ],
       [9.99, 3.99, 4.  ]])

Давайте пока пропустим вторую голову и сосредоточимся на окончательном результате первой головы. Ко второй голове мы вернёмся позже.

4.3 Вычисление внимания

Для вычисления показателя внимания требуется пара шагов:

  1. Вычисление скалярного произведения запроса и каждого ключа

  2. Деление результата на квадратный корень размерности вектора ключа

  3. Применение функции softmax для получения весов внимания

  4. Умножение каждого вектора значения на веса внимания

4.3.1 Скалярное произведение запроса и каждого ключа

Для вычисления результата для «Hello» необходимо вычислить скалярное произведение q1 и каждого вектора ключа (k1 и k2)

9d2504e2828fd8ea6d6c94e98d42be9a.png

В мире матриц это будет равно Q1, умноженному на перестановку K1

6e4a5525d96bde952b7b76024dc842d5.png

Я могу сделать ошибку, так что давайте проверим всё это ещё раз с помощью Python

scores1 = Q1 @ K1.T
scores1
array([[ 68.    , 105.21  ],
       [ 87.88  , 135.5517]])

4.3.2 Деление на квадратный корень размерности вектора ключа

Затем мы делим показатели на квадратный корень размерности (d) ключей (в данном случае это 3, но в научной статье она была равна 64). Почему? При больших значениях d скалярное произведение растёт слишком быстро (ведь мы складываем умножение кучи чисел, что приводит к большим значениям). А большие значения — это плохо! Подробнее мы поговорим об этом чуть позже.

scores1 = scores1 / np.sqrt(3)
scores1
array([[39.2598183 , 60.74302182],
       [50.73754166, 78.26081048]])

4.3.3 Применение функции softmax

Далее используем softmax для нормализации, чтобы все они были положительны и в сумме равнялись 1.

Что такое softmax?

Softmax — это функция, получающая вектор значений и возвращающая вектор значений между 0 и 1, в котором сумма значений равна 1. Это удобный способ получения вероятностей. Функция определяется следующим образом:

e7a48588f466c4234929d03def3500f0.png

Не пугайтесь этой формулы, на самом деле она довольно проста. Допустим, у нас есть следующий вектор:

c750d84109caee4305daf1dfafe58f80.png

Softmax этого вектора будет такой:

c6c21d57fe4f33b902add6e0b6bed43f.png

Как видите, все значения положительны и в сумме дают 1.

def softmax(x):
    return np.exp(x) / np.sum(np.exp(x), axis=1, keepdims=True)


scores1 = softmax(scores1)
scores1
array([[4.67695573e-10, 1.00000000e+00],
       [1.11377182e-12, 1.00000000e+00]])

4.3.4 Умножение матрицы значений на веса внимания

Далее мы умножаем на матрицу значений

attention1 = scores1 @ V1
attention1
array([[7.99, 8.84, 6.84],
       [7.99, 8.84, 6.84]])

Давайте объединим 4.3.1, 4.3.2, 4.3.3 и 4.3.4 в одну формулу с использованием матриц (это из раздела 3.2.1 научной статьи):

a02751d90c6c85873ce9b30671a9496a.png

Да, вот и всё! Все проделанные нами вычисления можно легко свести к показанной выше формуле внимания! Давайте перенесём это в код.

def attention(x, WQ, WK, WV):
    K = x @ WK
    V = x @ WV
    Q = x @ WQ

    scores = Q @ K.T
    scores = scores / np.sqrt(3)
    scores = softmax(scores)
    scores = scores @ V
    return scores
attention(embedding, WQ1, WK1, WV1)
array([[7.99, 8.84, 6.84],
       [7.99, 8.84, 6.84]])

Мы убедились, что значения те же, что и получены выше. Давайте воспользуемся этим кодом для получения показателей внимания второй головы внимания:

attention2 = attention(embedding, WQ2, WK2, WV2)
attention2
array([[8.84, 3.99, 7.99],
       [8.84, 3.99, 7.99]])

Если вас интересует, как внимание стало одинаковым для двух эмбеддингов, то это вызвано тем, что softmax переводит показатели в 0 и 1. Смотрите:

softmax(((embedding @ WQ2) @ (embedding @ WK2).T) / np.sqrt(3))
array([[1.10613872e-14, 1.00000000e+00],
       [4.95934510e-20, 1.00000000e+00]])

Это вызвано плохой инициализацией матриц и маленьким размерам векторов. Большие различиях в показателях до применения softmax будут лишь усилены, приводя к том, что одно значение будет близко к 1, а другие к 0. На практике наши исходные значения матрицы эмбеддингов были слишком велики, что привело к высоким значениям для ключей, значений и запросов, которые при умножении становились только выше.

Помните, как мы выполняли деление на квадратный корень размерности ключей? Именно поэтому мы это и делали, в противном случае значения скалярного произведения были бы слишком большими, из-за чего получились бы большие значения после softmax. Однако в данном случае, похоже, этого не было достаточно, учитывая наши небольшие значения! В качестве быстрого хака мы можем уменьшить масштаб значений на меньшее значение, чем квадратный корень трёх. Давайте переопределим функцию внимания, уменьшив масштаб на 30. В долгой перспективе это плохое решение, но оно поможет нам получить разные значения для показателей внимания. Позже мы вернёмся к более качественному решению.

def attention(x, WQ, WK, WV):
    K = x @ WK
    V = x @ WV
    Q = x @ WQ

    scores = Q @ K.T
    scores = scores / 30  # we just changed this
    scores = softmax(scores)
    scores = scores @ V
    return scores
attention1 = attention(embedding, WQ1, WK1, WV1)
attention1
array([[7.54348784, 8.20276657, 6.20276657],
       [7.65266185, 8.35857269, 6.35857269]])
attention2 = attention(embedding, WQ2, WK2, WV2)
attention2
array([[8.45589591, 3.85610456, 7.72085664],
       [8.63740591, 3.91937741, 7.84804146]])

4.3.5 Выходные значения внимания голов

Следующий слой кодировщика ожидает на входе одну матрицу, а не две. Первым этапом будет конкатенация выходных значений двух голов (см. раздел 3.2.2 научной статьи)

attentions = np.concatenate([attention1, attention2], axis=1)
attentions
array([[7.54348784, 8.20276657, 6.20276657, 8.45589591, 3.85610456,
        7.72085664],
       [7.65266185, 8.35857269, 6.35857269, 8.63740591, 3.91937741,
        7.84804146]])

Затем мы умножаем эту конкатенированную матрицу на матрицу весов, чтобы получить окончательный результат слоя внимания. Этой матрице весов модель тоже обучается! Размерность матрицы гарантирует, что мы вернёмся к той же размерности, что была у эмбеддинга (в нашем случае 4).

# Просто произвольные значения
W = np.array(
    [
        [0.79445237, 0.1081456, 0.27411536, 0.78394531],
        [0.29081936, -0.36187258, -0.32312791, -0.48530339],
        [-0.36702934, -0.76471963, -0.88058366, -1.73713022],
        [-0.02305587, -0.64315981, -0.68306653, -1.25393866],
        [0.29077448, -0.04121674, 0.01509932, 0.13149906],
        [0.57451867, -0.08895355, 0.02190485, 0.24535932],
    ]
)
Z = attentions @ W
Z
array([[ 11.46394285, -13.18016471, -11.59340253, -17.04387829],
       [ 11.62608573, -13.47454936, -11.87126395, -17.4926367 ]])

Всё это можно объединить в изображение из The Ilustrated Transformer

Attention
Attention

5. Слой с прямой связью

5.1 Простой слой с прямой связью

После слоя самовнимания у кодировщика идёт нейронная сеть с прямой связью (feed-forward neural network, FFN). Это простая сеть с двумя линейными преобразованиями и активацией ReLU между ними. В посте The Illustrated Transformer подробностей об этом нет, так что я вкратце объясню этот слой. Цель FFN заключается в обработке и трансформировании описания, созданного механизмом внимания. Поток обычно выглядит так (см. раздел 3.3 научной статьи):

  1. Первый линейный слой: обычно он расширяет размерность входных данных. Например, если размерность входных данных равна 512, то размерность выходных данных может быть равна 2048. Это выполняется для того, чтобы позволить модели изучать более сложные функции. В нашем простом примере с размерностью 4 мы расширимся до 8.

  2. Активация ReLU: нелинейная функция активации. Это простая функция, возвращающая 0, если входные данные отрицательны, и входные данные, если они положительны. Это позволяет модели обучаться нелинейным функциям. Вычисления выглядят так:

262eac2557430f65416a724b1505a335.png
  1. Второй линейный слой: он противоположен первому линейному слою. Этот слой снова возвращает размерность к исходной. В нашем примере он выполнит снижение с 8 до 4.

Всё это можно описать следующим образом

bbc6f12f046194f7a985ee22eeb560c8.png

Напомню, что входными данными для этого слоя является Z, которое мы вычислили в самовнимании. Вот какие значения мы там получили

98bd6018fe81f8a9ce807877020cc5d8.png

Теперь давайте зададим произвольные значения для матриц весов и векторов смещений. Я сделаю это в коде, но если у вас хватит терпения, то можете задать их вручную!

W1 = np.random.randn(4, 8)
W2 = np.random.randn(8, 4)
b1 = np.random.randn(8)
b2 = np.random.randn(4)

А теперь давайте запишем функцию прямого прохода

def relu(x):
    return np.maximum(0, x)

def feed_forward(Z, W1, b1, W2, b2):
    return relu(Z.dot(W1) + b1).dot(W2) + b2
output_encoder = feed_forward(Z, W1, b1, W2, b2)
output_encoder
array([[ -3.24115016,  -9.7901049 , -29.42555675, -19.93135286],
       [ -3.40199463,  -9.87245924, -30.05715408, -20.05271018]])

5.2 Объединяем всё: произвольный кодировщик

Теперь давайте напишем код, чтобы объединить в блоке кодировщика многоголовое внимание и прямую связь.

Примечание

Код оптимизирован для понимания и образовательных целей, а не для производительности, не судите слишком строго!

d_embedding = 4
d_key = d_value = d_query = 3
d_feed_forward = 8
n_attention_heads = 2

def attention(x, WQ, WK, WV):
    K = x @ WK
    V = x @ WV
    Q = x @ WQ

    scores = Q @ K.T
    scores = scores / np.sqrt(d_key)
    scores = softmax(scores)
    scores = scores @ V
    return scores

def multi_head_attention(x, WQs, WKs, WVs):
    attentions = np.concatenate(
        [attention(x, WQ, WK, WV) for WQ, WK, WV in zip(WQs, WKs, WVs)], axis=1
    )
    W = np.random.randn(n_attention_heads * d_value, d_embedding)
    return attentions @ W

def feed_forward(Z, W1, b1, W2, b2):
    return relu(Z.dot(W1) + b1).dot(W2) + b2

def encoder_block(x, WQs, WKs, WVs, W1, b1, W2, b2):
    Z = multi_head_attention(x, WQs, WKs, WVs)
    Z = feed_forward(Z, W1, b1, W2, b2)
    return Z

def random_encoder_block(x):
    WQs = [
        np.random.randn(d_embedding, d_query) for _ in range(n_attention_heads)
    ]
    WKs = [
        np.random.randn(d_embedding, d_key) for _ in range(n_attention_heads)
    ]
    WVs = [
        np.random.randn(d_embedding, d_value) for _ in range(n_attention_heads)
    ]
    W1 = np.random.randn(d_embedding, d_feed_forward)
    b1 = np.random.randn(d_feed_forward)
    W2 = np.random.randn(d_feed_forward, d_embedding)
    b2 = np.random.randn(d_embedding)
    return encoder_block(x, WQs, WKs, WVs, W1, b1, W2, b2)

Вспомним наши входные данные в матрице E, имеющие позиционное кодирование и эмбеддинг.

embedding
array([[1.  , 3.  , 3.  , 5.  ],
       [2.84, 3.99, 4.  , 6.  ]])

Теперь передадим это нашей функции random_encoder_block

random_encoder_block(embedding)
array([[ -71.76537515, -131.43316885,   13.2938131 ,   -4.26831998],
       [ -72.04253781, -131.84091347,   13.3385937 ,   -4.32872015]])

Отлично! Это был всего один блок кодировщика. В научной статье применяются шесть кодировщиков. Выходные данные одного кодировщика передаются на следующий и так далее:

def encoder(x, n=6):
    for _ in range(n):
        x = random_encoder_block(x)
    return x


encoder(embedding)
/tmp/ipykernel_11906/1045810361.py:2: RuntimeWarning: overflow encountered in exp
  return np.exp(x)/np.sum(np.exp(x),axis=1, keepdims=True)
/tmp/ipykernel_11906/1045810361.py:2: RuntimeWarning: invalid value encountered in divide
  return np.exp(x)/np.sum(np.exp(x),axis=1, keepdims=True)
array([[nan, nan, nan, nan],
       [nan, nan, nan, nan]])

5.3 Остаточные связи и нормализация слоёв

Ой-ёй! У нас начали появляться NaN! Похоже, наши значения слишком велики и при передаче следующему кодировщику они оказываются слишком большими и «взрываются»! Эта проблема слишком больших значений часто возникает при обучении моделей. Например, когда мы выполняем обратное распространение ошибки (методику, при помощи которой модели обучаются), градиенты могут оказаться слишком большими и в результате «взрываются»; это называется взрывом градиентов (gradient explosion). Без нормализации небольшие изменения во входных данных на первых слоях в последующих слоях усиливаются. Это распространённая проблема в глубоких нейросетях. Существует два способа борьбы с этой проблемой: остаточные связи и нормализация слоёв (они вкратце упоминаются в разделе 3.1 научной статьи).

  • Остаточные связи просто прибавляют входные данные слоя к его выходным данным. Например, мы складываем исходный эмбеддинг с выходными данными внимания. Остаточные связи устраняют проблему исчезающих градиентов. Логика в том, что если градиент слишком мал, то мы можем просто сложить входные данные к выходным, и градиент станет больше. Вычисления очень просты:

f57ea26cb87a7dc176fe66b656dc2bbb.png

Вот и всё! Мы сделаем это для выходных данных внимания и выходных данных слоя с прямой связью.

  • Нормализация слоя — это методика нормализации входных данных слоя. Она выполняет нормализацию по размерности эмбеддинга. Логика в том, что мы хотим нормализовать входные значения слоя, чтобы они имели среднее значение 0 и квадратическое отклонение 1. Это помогает с градиентным потоком. Вычисления на первый взгляд выглядят не так уж просто.

e86b11dab9af842f994c4919c2e5d7ab.png

Давайте объясним каждый параметр:

  • μ — это среднее значение эмбеддинга

  • σ — это квадратическое отклонение эмбеддинга

  • ε — это малое число, чтобы избежать деления на ноль. В случае нулевого значения квадратичного отклонения этот маленький эпсилон спасает нас.

  • γ и β — это изучаемые параметры, управляющие этапами масштабирования и сдвига.

В отличие от пакетной нормализации (batch normalization, не волнуйтесь, если не знаете, что это такое), нормализация слоёв нормализует по размерности эмбеддинга; это означает, что на каждый эмбеддинг не будут влиять другие сэмплы в пакете. Идея заключается в том, что мы хотим нормализовать входные данные слоя, чтобы они имели среднее значение 0 и квадратичное отклонение 1.

Зачем мы добавляем изучаемые параметры γ и β? Причина в том, что мы не хотим терять силу представления слоя. Если просто нормализовать входные данные, то какая-то информация может потеряться. Добавляя изучаемые параметры, мы можем научиться масштабировать и сдвигать нормализованные значения.

Соединив эти уравнения, мы получим уравнение для всего кодировщика:

a0ac41a886c0c090a94831b723273008.png

Давайте проверим его на нашем примере! Возьмём прежние значения E и Z:

93bf47f27dedfcf295a42d2a389532c0.png

Теперь давайте вычислим нормализацию слоя; можно разделить этот процесс на три этапа:

  1. Вычисление среднего и дисперсии для каждого эмбеддинга.

  2. Нормализация вычитанием среднего в своей строке и делением на квадратный корень дисперсии строки (плюс малое число, чтобы избежать деления на ноль).

  3. Масштабирование и сдвиг умножением на гамму и прибавлением беты.

5.3.1 Среднее и дисперсия

Для первого эмбеддинга

7612e4d1500e7da378314073941be8ec.png

То же самое можно сделать для второго эмбеддинга. Пропустим сами вычисления и покажем только результат.

18f35a79565b79570fe341e8b6d85172.png

Давайте проверим при помощи Python

(embedding + Z).mean(axis=-1, keepdims=True)
array([[-4.58837567],
       [-3.59559107]])
(embedding + Z).std(axis=-1, keepdims=True)
array([[ 9.92061529],
       [10.50653019]])

Отлично! Теперь нормализуем

5.3.2 Нормализация

При нормализации из каждого значения в эмбеддинге мы вычитаем среднее и делим его на квадратичное отклонение. Эпсилон — это очень маленькое значение, например, 0,00001. Чтобы упростить, будем считать, что γ = 1, а β = 0.

ffe25dfe71f08897906a58c82bd44a0f.png

Для второго эмбеддинга мы не будем выполнять вычисления вручную. Проверим их при помощи кода. Переопределим функцию encoder_block, внеся следующее изменение:

def layer_norm(x, epsilon=1e-6):
    mean = x.mean(axis=-1, keepdims=True)
    std = x.std(axis=-1, keepdims=True)
    return (x - mean) / (std + epsilon)

def encoder_block(x, WQs, WKs, WVs, W1, b1, W2, b2):
    Z = multi_head_attention(x, WQs, WKs, WVs)
    Z = layer_norm(Z + x)

    output = feed_forward(Z, W1, b1, W2, b2)
    return layer_norm(output + Z)
layer_norm(Z + embedding)
array([[ 1.71887693, -0.56365339, -0.40370747, -0.75151608],
       [ 1.71909039, -0.56050453, -0.40695381, -0.75163205]])

Сработало! Давайте ещё раз попробуем пропустить эмбеддинг через шесть кодировщиков.

def encoder(x, n=6):
    for _ in range(n):
        x = random_encoder_block(x)
    return x


encoder(embedding)
array([[-0.335849  , -1.44504571,  1.21698183,  0.56391289],
       [-0.33583947, -1.44504861,  1.21698606,  0.56390202]])

Отлично! Значения приемлемые и отсутствуют NaN! Идея стека кодировщиков заключается в том, что на выходе они выдают непрерывное описание z, передающее смысл входной последовательности. Затем это описание передаётся декодеру, который генерирует выходную последовательность символов по одному элементу за раз.

Прежде чем приступать к декодеру, взглянем на изображение из потрясающего поста Джея:

Кодировщик и декодер
Кодировщик и декодер

Каждый из элементов в левой части должен быть вам уже понятен! Впечатляет, правда? А теперь давайте перейдём к декодеру.

Декодер

Большинство знаний, полученных при изучении кодировщиков, будет использоваться и в декодере! Декодер имеет два слоя самовнимания, один для кодировщика, другой для декодера. Также декодер имеет слой с прямой связью. Давайте разберём каждую из частей по порядку.

Блок декодера получает два элемента входных данных: выходные данные кодировщика и сгенерированную выходную последовательность. Выходные данные кодировщика — это описание входной последовательности. В процессе инференса сгенерированная выходная последовательность начинается с особого токена начала последовательности (start-of-sequence token, SOS). Во время обучения целевая выходная последовательность — это действительная выходная последовательность, сдвинутая на одну позицию. Скоро это станет вам понятнее!

Имея сгенерированный кодировщиком эмбеддинг и токен SOS, декодер генерирует следующий токен последовательности, то есть «hola». Декодер авторегрессивен, то есть он берёт ранее сгенерированные токены и снова генерирует второй токен.

  • Итерация 1: входные данные — SOS, выходные — «hola»

  • Итерация 2: входные данные — SOS + «hola», выходные — «mundo»

  • Итерация 3: входные данные — SOS + «hola» + «mundo», выходные — EOS

Здесь SOS — это токен начала последовательности, а EOS — токен конца последовательности. После генерации токена EOS декодер прекращает работу. Он генерирует по одному токену за раз. Обратите внимание, что во всех итерациях используется эмбеддинг, сгенерированный кодировщиком.

Примечание

Такая авторегрессивная структура замедляет работу декодера. Кодировщик способен генерировать свой эмбеддинг за один прямой проход, а декодеру необходимо выполнить множество прямых проходов. Это одна из причин, по которым архитектуры, использующие один кодировщик (например, BERT или модели схожести предложений) гораздо быстрее, чем архитектуры с одними только декодерами (например, GPT-2 или BART).

Давайте разберём каждый из этапов! Как и кодировщик, декодер состоит из стека блоков декодеров. Блок декодера чуть сложнее, чем блок кодировщика. Его общая структура такова:

  1. Слой самовнимания (маскированный)

  2. Остаточная связь и нормализация слоя

  3. Слой внимания кодировщика-декодера

  4. Остаточная связь и нормализация слоя

  5. Слой с прямой связью

  6. Остаточная связь и нормализация слоя

Мы уже знакомы со всей математикой пунктов 1, 2, 3, 5 и 6. Взглянув на правую часть изображения ниже, вы увидите, что все эти блоки вам уже известны :

Модель трансформера из статьи «Attention is all you need»
Модель трансформера из статьи «Attention is all you need»

1. Эмбеддинг текста

Первый текст декодера нужен для эмбеддинга входных токенов. Входным токеном является SOS, так что мы выполняем его эмбеддинг. Используется та же размерность эмбеддинга, что и для кодировщика. Предположим, вектор эмбеддинга для SOS имеет такой вид:

35f571ab480469598afaf2272b2ac2ea.png

2. Позиционное кодирование

Теперь мы добавим в эмбеддинг позиционное кодирование, как делали это в случае с кодировщиком. Учитывая, что это так же позиция, что и у «Hello», у нас будет то же позиционное кодирование, что и раньше:

  • i = 0 (чётный): PE(0,0) = sin(0 / 10000^(0 / 4)) = sin(0) = 0

  • i = 1 (нечётный): PE(0,1) = cos(0 / 10000^(2*1 / 4)) = cos(0) = 1

  • i = 2 (чётный): PE(0,2) = sin(0 / 10000^(2*2 / 4)) = sin(0) = 0

  • i = 3 (нечётный): PE(0,3) = cos(0 / 10000^(2*3 / 4)) = cos(0) = 1

3. Сложение позиционного кодирования и эмбеддинга

Сложение позиционного кодирования с эмбеддингом выполняется сложением двух векторов:

94c8d59a4656853cd52979ac450b716b.png

4. Самовнимание

Первый этап в блоке декодера — это механизм самовнимания. К счастью, у нас есть для этого код и мы можем просто его использовать!

d_embedding = 4
n_attention_heads = 2

E = np.array([[1, 1, 0, 1]])
WQs = [np.random.randn(d_embedding, d_query) for _ in range(n_attention_heads)]
WKs = [np.random.randn(d_embedding, d_key) for _ in range(n_attention_heads)]
WVs = [np.random.randn(d_embedding, d_value) for _ in range(n_attention_heads)]

Z_self_attention = multi_head_attention(E, WQs, WKs, WVs)
Z_self_attention
array([[ 2.19334924, 10.61851198, -4.50089666, -2.76366551]])

Примечание

С точки зрения инференса всё довольно просто, однако с точки зрения обучения есть сложности. При обучении мы используем неразмеченные данные: просто кучу текстовых данных, которые собираем частым скрейпингом в вебе. Цель кодировщика — передача всей информации входных данных, а задача декодера —предсказание следующего наиболее вероятного токена. Это значит, что декодер может использовать только ранее сгенерированные токены (он не может схитрить и посмотреть следующие токены).

Из-за этого мы используем маскированное самовнимание: маскируем ещё не сгенерированные токены. Это выполняется присвоением показателям внимания значений -inf. Так делается в научной статье (раздел 3.2.3.1). Пока мы это пропустим, но важно помнить, что при обучении декодер чуть сложнее.

5. Остаточные связи и нормализация слоёв

Здесь нет ничего таинственного, мы просто складываем входные данные с выходными данными самовнимания и применяем нормализацию слоя. Используется тот же код, что и выше.

Z_self_attention = layer_norm(Z_self_attention + E)
Z_self_attention
array([[ 0.17236212,  1.54684892, -1.0828824 , -0.63632864]])

6. Внимание кодировщика-декодера

Эта часть новая! Если вы задавались вопросом, куда направляются генерируемые кодировщиком эмбеддинги, то сейчас самое время для них!

Предположим, что выходными данными кодировщика является такая матрица:

fc2024fb11fec40a9e7153c6615fc0ce.png

В механизме самовнимания мы вычисляем запросы, ключи и значения для входного эмбеддинга.

Во внимании кодировщика-декодера мы вычисляем запросы из предыдущего слоя декодера и ключи и значения из выходных данных кодировщика! Все вычисления остаются такими же, что и раньше; единственное отличие в том, какой эмбеддинг использовать для запросов. Давайте взглянем на код

def encoder_decoder_attention(encoder_output, attention_input, WQ, WK, WV):
    # В следующих трёх строках и состоит основное различие!
    K = encoder_output @ WK    # Обратите внимание, что теперь мы передаём предыдущие выходные данные кодировщика!
    V = encoder_output @ WV    # Обратите внимание, что теперь мы передаём предыдущие выходные данные кодировщика!
    Q = attention_input @ WQ   # То же, что и для самовнимания

    # Остаётся таким же
    scores = Q @ K.T
    scores = scores / np.sqrt(d_key)
    scores = softmax(scores)
    scores = scores @ V
    return scores


def multi_head_encoder_decoder_attention(
    encoder_output, attention_input, WQs, WKs, WVs
):
    # Обратите внимание, что теперь мы передаём предыдущие выходные данные кодировщика!
    attentions = np.concatenate(
        [
            encoder_decoder_attention(
                encoder_output, attention_input, WQ, WK, WV
            )
            for WQ, WK, WV in zip(WQs, WKs, WVs)
        ],
        axis=1,
    )
    W = np.random.randn(n_attention_heads * d_value, d_embedding)
    return attentions @ W
WQs = [np.random.randn(d_embedding, d_query) for _ in range(n_attention_heads)]
WKs = [np.random.randn(d_embedding, d_key) for _ in range(n_attention_heads)]
WVs = [np.random.randn(d_embedding, d_value) for _ in range(n_attention_heads)]

encoder_output = np.array([[-1.5, 1.0, -0.8, 1.5], [1.0, -1.0, -0.5, 1.0]])

Z_encoder_decoder = multi_head_encoder_decoder_attention(
    encoder_output, Z_self_attention, WQs, WKs, WVs
)
Z_encoder_decoder
array([[ 1.57651431,  4.92489307, -0.08644448, -0.46776051]])

Сработало! Возможно, вы зададитесь вопросом: «зачем мы это делаем?». Дело в том, что мы хотим, чтобы декодер сосредоточился на релевантных частях входного текста (то есть «hello world»). Внимание кодировщика-декодера позволяет каждой позиции в декодере посетить все позиции входной последовательности. Это очень полезно для таких задач, как перевод, когда декодеру нужно сосредоточиться на релевантных частях входной последовательности. Декодер будет учиться сосредотачиваться на релевантных частях входной последовательности, учась генерировать правильные выходные токены. Это очень мощный механизм!

7. Остаточные связи и нормализация слоя

Всё то же, что и раньше!

Z_encoder_decoder = layer_norm(Z_encoder_decoder + Z_self_attention)
Z_encoder_decoder
array([[-0.44406723,  1.6552893 , -0.19984632, -1.01137575]])

8. Слой с прямой связью

И тут то же самое! После этого я также выполню остаточную связь и нормализацию слоя.

W1 = np.random.randn(4, 8)
W2 = np.random.randn(8, 4)
b1 = np.random.randn(8)
b2 = np.random.randn(4)

output = layer_norm(feed_forward(Z_encoder_decoder, W1, b1, W2, b2) + Z_encoder_decoder)
output
array([[-0.97650182,  0.81470137, -2.79122044, -3.39192873]])

9. Объединяем всё: произвольный декодер

Давайте напишем код для одного блока декодера. Самое главное изменение заключается в том, что теперь у нас есть дополнительный механизм внимания.

d_embedding = 4
d_key = d_value = d_query = 3
d_feed_forward = 8
n_attention_heads = 2
encoder_output = np.array([[-1.5, 1.0, -0.8, 1.5], [1.0, -1.0, -0.5, 1.0]])

def decoder_block(
    x,
    encoder_output,
    WQs_self_attention, WKs_self_attention, WVs_self_attention,
    WQs_ed_attention, WKs_ed_attention, WVs_ed_attention,
    W1, b1, W2, b2,
):
    # То же, что и раньше
    Z = multi_head_attention(
        x, WQs_self_attention, WKs_self_attention, WVs_self_attention
    )
    Z = layer_norm(Z + x)

    # Основное различие заключается в следующих трёх строках!
    Z_encoder_decoder = multi_head_encoder_decoder_attention(
        encoder_output, Z, WQs_ed_attention, WKs_ed_attention, WVs_ed_attention
    )
    Z_encoder_decoder = layer_norm(Z_encoder_decoder + Z)

    # То же, что и раньше
    output = feed_forward(Z_encoder_decoder, W1, b1, W2, b2)
    return layer_norm(output + Z_encoder_decoder)

def random_decoder_block(x, encoder_output):
    # Просто несколько произвольных инициализаций
    WQs_self_attention = [
        np.random.randn(d_embedding, d_query) for _ in range(n_attention_heads)
    ]
    WKs_self_attention = [
        np.random.randn(d_embedding, d_key) for _ in range(n_attention_heads)
    ]
    WVs_self_attention = [
        np.random.randn(d_embedding, d_value) for _ in range(n_attention_heads)
    ]

    WQs_ed_attention = [
        np.random.randn(d_embedding, d_query) for _ in range(n_attention_heads)
    ]
    WKs_ed_attention = [
        np.random.randn(d_embedding, d_key) for _ in range(n_attention_heads)
    ]
    WVs_ed_attention = [
        np.random.randn(d_embedding, d_value) for _ in range(n_attention_heads)
    ]

    W1 = np.random.randn(d_embedding, d_feed_forward)
    b1 = np.random.randn(d_feed_forward)
    W2 = np.random.randn(d_feed_forward, d_embedding)
    b2 = np.random.randn(d_embedding)


    return decoder_block(
        x, encoder_output,
        WQs_self_attention, WKs_self_attention, WVs_self_attention,
        WQs_ed_attention, WKs_ed_attention, WVs_ed_attention,
        W1, b1, W2, b2,
    )
def decoder(x, decoder_embedding, n=6):
    for _ in range(n):
        x = random_decoder_block(x, decoder_embedding)
    return x

decoder(E, encoder_output)
array([[ 0.25919176,  1.49913566, -1.14331487, -0.61501256],
       [ 0.25956188,  1.49896896, -1.14336934, -0.61516151]])

Генерация выходной последовательности

У нас уже есть все необходимые части! Давайте сгенерируем выходную последовательность.

  • У нас есть кодировщик, получающий входную последовательность и генерирующий его обогащённое описание. Он состоит из стека блоков кодировщиков.

  • У нас есть декодер, получающий выходные данные кодировщика и сгенерированные токены и генерирующий выходную последовательность. Он состоит из стека блоков декодеров.

Как перейти от выходных данных декодера к слову? Нужно добавить поверх декодера последний линейный слой и слой softmax. Весь алгоритм в целом выглядит так:

  1. Обработка кодировщиком: кодировщик получает входную последовательность и генерирует контекстуализированное описание всего предложения при помощи стека блоков кодировщиков.

  2. Инициализация декодера: процесс декодирования начинается с эмбеддинга токена SOS (Start of Sequence), соединённого с выходными данными кодировщика.

  3. Работа декодера: декодер использует выходные данные кодировщика и эмбеддинги всех ранее сгенерированных токенов для создания нового списка эмбеддингов.

  4. Линейный слой для логитов: линейный слой применяется к последнему выходному эмбеддингу декодера для генерации логитов, представляющих сырые предсказания следующего токена.

  5. Softmax для вероятностей: затем эти логиты передаются через слой softmax, преобразующий их в распределение вероятностей по потенциальным следующим токенам.

  6. Итеративная генерация токенов: этот процесс повторяется, и на каждом этапе декодер генерирует следующий токен на основании кумулятивных эмбеддингов ранее сгенерированных токенов и исходных выходных данных кодировщика.

  7. Формирование предложения: эти этапы генерации продолжаются, пока не будет создан токен EOS (End of Sequence) или не достигнута заранее заданная максимальная длина предложения.

Об этом говорится в разделе 3.4 научной статьи.

1. Линейный слой

Линейный слой — это простое линейное преобразование. Он получает выходные данные декодера и преобразует их в вектор размера vocab_size. Это размер словаря. Например, если у нас есть словарь из 10000 слов, то линейный слой преобразовал бы выходные данные декодера в вектор размера 10000. Этот вектор содержал бы вероятность того, что каждое слово будет следующим словом в последовательности. Для простоты можно начать со словаря из 10 слов и предположить, что первые выходные данные декодера — это очень простой вектор: [1, 0, 1, 0]. Мы используем произвольные веса и матрицы перекосов размера vocab_size x decoder_output_size.

def linear(x, W, b):
    return np.dot(x, W) + b

x = linear([1, 0, 1, 0], np.random.randn(4, 10), np.random.randn(10))
x
array([ 0.06900542, -1.81351091, -1.3122958 , -0.33197364,  2.54767851,
       -1.55188231,  0.82907169,  0.85910931, -0.32982856, -1.26792439])

Примечание

Что используется в качестве входных данных для линейного слоя? Декодер будет выводить по одному эмбеддингу для каждого токена в последовательности. Входными данными для линейного слоя станет последний сгенерированный эмбеддинг. Последний эмбеддинг включает в себя информацию для всей последовательности до этого этапа, то есть содержит всю информацию, необходимую для генерации следующего токена. Это значит, что каждый выходной эмбеддинг декодера содержит информацию о всей последовательности до этого этапа.

2. Softmax

Они называются логитами, но интерпретировать их не так просто. Для получения вероятностей можно применить функцию softmax.

softmax(x)
array([[0.01602618, 0.06261303, 0.38162024, 0.03087794, 0.0102383 ,
        0.00446011, 0.01777314, 0.00068275, 0.46780959, 0.00789871]])

И так мы получили вероятности! Предположим, словарь имеет такой вид:

af1ce2cd67a1bfc1e3def62b9b09cc96.png

Мы видим, что вероятности таковы:

  • hello: 0.01602618

  • mundo: 0.06261303

  • world: 0.38162024

  • how: 0.03087794

  • ?: 0.0102383

  • EOS: 0.00446011

  • SOS: 0.01777314

  • a: 0.00068275

  • hola: 0.46780959

  • c: 0.00789871

Из этого видно, что наиболее вероятный следующий токен — это «hola». Если всегда выбирается наиболее вероятный токен, это называется жадным декодингом. Это не всегда наилучший подход, потому что он может привести к субоптимальным результатам, но пока мы не будем сейчас углубляться в методики генерации. Если хотите узнать о них подробнее, то прочитайте потрясающий пост.

3. Случайный трансформер из кодировщика и декодера

Давайте напишем код целиком. Зададим словарь, сопоставляющий слова с их изначальными эмбеддингами. Надо отменить, что это тоже изучается при обучении, но пока мы используем случайные значения.

vocabulary = [
    "hello",
    "mundo",
    "world",
    "how",
    "?",
    "EOS",
    "SOS",
    "a",
    "hola",
    "c",
]
embedding_reps = np.random.randn(10, 4)
vocabulary_embeddings = {
    word: embedding_reps[i] for i, word in enumerate(vocabulary)
}
vocabulary_embeddings
{'hello': array([-0.32106406,  2.09332588, -0.77994069,  0.92639774]),
 'mundo': array([-0.59563791, -0.63389256,  1.70663692, -0.99495115]),
 'world': array([ 1.35581862, -0.0323546 ,  2.76696887,  0.83069982]),
 'how': array([-0.52975474,  0.94439644,  0.80073818, -1.50135518]),
 '?': array([-0.88116833,  0.13995055,  2.01827674, -0.52554391]),
 'EOS': array([1.12207024, 1.40905796, 1.22231714, 0.02267638]),
 'SOS': array([-0.60624082, -0.67560165,  0.77152125,  0.63472247]),
 'a': array([ 1.67622229, -0.20319309, -0.18324905, -0.24258774]),
 'hola': array([ 1.07809402, -0.83846408, -0.33448976,  0.28995976]),
 'c': array([ 0.65643157,  0.24935726, -0.80839751, -1.87156293])}

А теперь напишем произвольный метод generate , авторегрессивно генерирующий токены.

def generate(input_sequence, max_iters=3):
    # Сначала мы кодируем входные данные в эмбеддинги
    # Для простоты мы пропустим этап позиционного кодирования
    embedded_inputs = [
        vocabulary_embeddings[token] for token in input_sequence
    ]
    print("Embedding representation (encoder input)", embedded_inputs)

    # Затем генерируем описание эмбеддинга
    encoder_output = encoder(embedded_inputs)
    print("Embedding generated by encoder (encoder output)", encoder_output)

    # Инициализируем выходные данные декодера эмбеддингом начального токена
    sequence_embeddings = [vocabulary_embeddings["SOS"]]
    output = "SOS"
    
    # Случайные матрицы для линейного слоя
    W_linear = np.random.randn(d_embedding, len(vocabulary))
    b_linear = np.random.randn(len(vocabulary))

    # Мы ограничиваем количество этапов декодинга, чтобы избежать слишком последовательностей без EOS
    for i in range(max_iters):
        # Этап декодера
        decoder_output = decoder(sequence_embeddings, encoder_output)

        # Используем для предсказания только последние выходные данные
        logits = linear(decoder_output[-1], W_linear, b_linear)
        # Обёртываем логиты в список, потому что softmax нужны пакеты/2D-массив
        probs = softmax([logits])

        # Получаем наиболее вероятный следующий токен
        next_token = vocabulary[np.argmax(probs)]
        sequence_embeddings.append(vocabulary_embeddings[next_token])
        output += " " + next_token

        print(
            "Iteration", i, 
            "next token", next_token,
            "with probability of", np.max(probs),
        )

        # Если следующий токен последний, то возвращаем последовательность
        if next_token == "EOS":
            return output

    return output, sequence_embeddings

Давайте запустим код!

generate(["hello", "world"])
Embedding representation (encoder input) [array([-0.32106406,  2.09332588, -0.77994069,  0.92639774]), array([ 1.35581862, -0.0323546 ,  2.76696887,  0.83069982])]
Embedding generated by encoder (encoder output) [[ 1.14747807 -1.5941759   0.36847675  0.07822107]
 [ 1.14747705 -1.59417696  0.36847441  0.07822551]]
Iteration 0 next token hola with probability of 0.4327111653266739
Iteration 1 next token mundo with probability of 0.4411354383451089
Iteration 2 next token world with probability of 0.4746898792307499
('SOS hola mundo world',
 [array([-0.60624082, -0.67560165,  0.77152125,  0.63472247]),
  array([ 1.07809402, -0.83846408, -0.33448976,  0.28995976]),
  array([-0.59563791, -0.63389256,  1.70663692, -0.99495115]),
  array([ 1.35581862, -0.0323546 ,  2.76696887,  0.83069982])])

Отлично, теперь у нас есть токены «how», «a» и «c». Это неправильный перевод, но этого вполне можно было ожидать, ведь веса мы использовали случайные.

Советую ещё раз подробно изучить всю архитектуру кодировщика-декодера из научной статьи:

Кодировщик и декодер
Кодировщик и декодер

Заключение

Надеюсь, пост показался вам интересным и информативным! Мы рассмотрели множество аспектов. Но разве это всё? На самом деле, практически да! В архитектуры новых трансформеров добавляют множество трюков, но фундамент трансформера именно таков, каким мы его описали. В зависимости от задачи также можно использовать только кодировщик или декодер. Например, в задачах, требующих понимания, например, в классификации, можно использовать стек кодировщиков с линейным слоем поверх него. Для задач, требующих генерации, например, в переводе, можно использовать стеки кодировщиков и декодеров. А для свободной генерации, например, как в ChatGPT или Mistral, можно применять только стек декодеров.

Разумеется, мы многое упростили. Давайте вкратце проверим, какие были числа в научной статье о трансформере:

  • Размерность эмбеддингов: 512 (в нашем примере 4)

  • Количество кодировщиков: 6 (в нашем примере 6)

  • Количество декодеров: 6 (в нашем примере 6)

  • Размерность прямой связи: 2048 (в нашем примере 8)

  • Количество голов внимания: 8 (в нашем примере 2)

  • Размерность внимания: 64 (в нашем примере 3)

Мы рассмотрели множество тем, но довольно интересно, то мы можем достичь впечатляющих результатов, увеличив масштабы этих вычислений и проведя умное обучение. Мы не рассмотрели в посте обучение, потому что наша цель заключалась в понимании вычислений при использовании готовой модели, но я надеюсь, что это станет надёжным фундаментом для перехода к обучению!

Также можно найти более формальный документ с вычислениями в этом PDF.

Упражнения

Вот несколько упражнений, чтобы попрактиковаться в понимании трансформера.

  1. В чём предназначение позиционного кодирования?

  2. Чем отличаются самовнимание и внимание кодировщика-декодера?

  3. Что произойдёт, если размерность внимания слишком мала? А если слишком велика?

  4. Вкратце опишите структуру слоя с прямой связью.

  5. Почему декодер медленнее кодировщика?

  6. Какова цель остаточных связей и нормализации слоёв?

  7. Как выполняется переход от выходных данных декодера к вероятностям?

  8. Почему выбор каждый раз самого вероятного следующего токена может вызвать проблемы?

Ресурсы

Источник

  • 09.10.25 08:37 pHqghUme

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  • 17.10.25 21:42 marcushenderson624

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  • 21.10.25 08:39 debby131

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  • 21.10.25 11:45 harristhomas7376

    "In the crypto world, this is great news I want to share. Last year, I fell victim to a scam disguised as a safe investment option. I have invested in crypto trading platforms for about 10yrs thinking I was ensuring myself a retirement income, only to find that all my assets were either frozen, I believed my assets were secure — until I discovered that my BTC funds had been frozen and withdrawals were impossible. It was a devastating moment when I realized I had been scammed, and I thought my Bitcoin was gone forever, Everything changed when a close friend recommended the Capital Crypto Recover Service. Their professionalism, expertise, and dedication enabled me to recover my lost Bitcoin funds back — more than €560.000 DEM to my BTC wallet. What once felt impossible became a reality thanks to their support. If you have lost Bitcoin through scams, hacking, failed withdrawals, or similar challenges, don’t lose hope. I strongly recommend Capital Crypto Recover Service to anyone seeking a reliable and effective solution for recovering any wallet assets. They have a proven track record of successful reputation in recovering lost password assets for their clients and can help you navigate the process of recovering your funds. Don’t let scammers get away with your hard-earned money – contact Email: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 21.10.25 11:45 harristhomas7376

    "In the crypto world, this is great news I want to share. Last year, I fell victim to a scam disguised as a safe investment option. I have invested in crypto trading platforms for about 10yrs thinking I was ensuring myself a retirement income, only to find that all my assets were either frozen, I believed my assets were secure — until I discovered that my BTC funds had been frozen and withdrawals were impossible. It was a devastating moment when I realized I had been scammed, and I thought my Bitcoin was gone forever, Everything changed when a close friend recommended the Capital Crypto Recover Service. Their professionalism, expertise, and dedication enabled me to recover my lost Bitcoin funds back — more than €560.000 DEM to my BTC wallet. What once felt impossible became a reality thanks to their support. If you have lost Bitcoin through scams, hacking, failed withdrawals, or similar challenges, don’t lose hope. I strongly recommend Capital Crypto Recover Service to anyone seeking a reliable and effective solution for recovering any wallet assets. They have a proven track record of successful reputation in recovering lost password assets for their clients and can help you navigate the process of recovering your funds. Don’t let scammers get away with your hard-earned money – contact Email: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 22.10.25 04:48 MATT PHILLIP

    I never imagined I’d fall for a crypto romance scam but it happened. Over the course of a few months, I sent nearly $150,000 worth of Bitcoin to someone I genuinely believed I was building a future with. When they disappeared without a trace, I was left heartbroken, humiliated, and financially devastated. For a long time, I didn’t tell anyone. I felt ashamed. But eventually, while searching for answers, I came across a Reddit thread that mentioned Agent Jasmine Lopez. I reached out, not expecting much. To my surprise, she treated me with kindness, not judgment. She used advanced tools like blockchain forensics, IP tracing, and smart contract analysis and with persistence and legal support, she was able to recover nearly 85% of what I lost. I know not everyone gets that kind of outcome, but thanks to [email protected] WhatsApp at +44 736-644-5035, I’ve started to reclaim not just my assets, but my confidence and peace of mind. If you’re going through something similar, you’re not alone and there is hope.

  • 22.10.25 07:36 donnacollier

    HOW I RECOVERED MY BITCOIN FROM CRYPTO INVESTMENT SCAM HOW I RECOVERED MY BITCOIN FROM CRYPTO INVESTMENT SCAM Hello everyone l’m by name Donna collier I live in urbandale 3 weeks ago was the darkest days of my life, i invested my hard earned money the sum of $123,000 into a crypto currency platform I was introduced to by a friend I met online everything happen so fast I was promised 300% of return of investment when it was time for me to cash out my investment and profit the platform was down I was so diversitated confused and tried to end it all then I came across upswing Ai a renowned expert in crypto currency and digital assets recovery at first it seem impossible after taking up my case within the the next 48 hours they where able to track down those fraud stars and recover my money I can’t recommend them enough to any one facing likewise change I will recommend you contact upswing Ai on Contact Details: WhatsApp +,1,2,0,2,8,1,0,1,4,0,7 E m a i l @Upswing-ai.com Website https: // u psw ing-ai. com/ platform /

  • 22.10.25 11:59 elizabethrush89

    God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover Via Contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 22.10.25 11:59 elizabethrush89

    God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover Via Contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 22.10.25 16:31 MATT PHILLIP

    I never imagined I’d fall for a crypto romance scam but it happened. Over the course of a few months, I sent nearly $150,000 worth of Bitcoin to someone I genuinely believed I was building a future with. When they disappeared without a trace, I was left heartbroken, humiliated, and financially devastated. For a long time, I didn’t tell anyone. I felt ashamed. But eventually, while searching for answers, I came across a Reddit thread that mentioned Agent Jasmine Lopez. I reached out, not expecting much. To my surprise, she treated me with kindness, not judgment. She used advanced tools like blockchain forensics, IP tracing, and smart contract analysis and with persistence and legal support, she was able to recover nearly 85% of what I lost. I know not everyone gets that kind of outcome, but thanks to [email protected] WhatsApp at +44 736-644-5035, I’ve started to reclaim not just my assets, but my confidence and peace of mind. If you’re going through something similar, you’re not alone and there is hope.

  • 23.10.25 01:52 marcushenderson624

    Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 23.10.25 01:52 marcushenderson624

    Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 23.10.25 15:47 MATT PHILLIP

    I never imagined I’d fall for a crypto romance scam but it happened. Over the course of a few months, I sent nearly $150,000 worth of Bitcoin to someone I genuinely believed I was building a future with. When they disappeared without a trace, I was left heartbroken, humiliated, and financially devastated. For a long time, I didn’t tell anyone. I felt ashamed. But eventually, while searching for answers, I came across a Reddit thread that mentioned Agent Jasmine Lopez. I reached out, not expecting much. To my surprise, she treated me with kindness, not judgment. She used advanced tools like blockchain forensics, IP tracing, and smart contract analysis and with persistence and legal support, she was able to recover nearly 85% of what I lost. I know not everyone gets that kind of outcome, but thanks to [email protected] WhatsApp at +44 736-644-5035, I’ve started to reclaim not just my assets, but my confidence and peace of mind. If you’re going through something similar, you’re not alone and there is hope.

  • 23.10.25 21:43 patricialovick86

    How To Recover Your Bitcoin Without Falling Victim To Scams: A  Testimony Experience With Capital Crypto Recover Services, Contact Telegram: @Capitalcryptorecover Dear Everyone, I would like to take a moment to share my positive experience with Capital Crypto Recover Services. Initially, I was unsure if it would be possible to recover my stolen bitcoins. However, with their expertise and professionalism, I was able to fully recover my funds. Unfortunately, many individuals fall victim to scams in the cryptocurrency space, especially those involving fraudulent investment platforms. However, I advise caution, as not all recovery services are legitimate. I personally lost $273,000 worth of Bitcoin from my Binance account due to a deceptive platform. If you have suffered a similar loss, you may be considering crypto recovery, The Capital Crypto Recover is the most knowledgeable and effective Capital Crypto Recovery Services assisted me in recovering my stolen funds within 24 hours, after getting access to my wallet. Their service was not only prompt but also highly professional and effective, and many recovery services may not be trustworthy. Therefore, I highly recommend Capital Crypto Recover to you. i do always research and see reviews about their service, For assistance finding your misplaced cryptocurrency, get in touch with them, They do their jobs quickly and excellently, Stay safe and vigilant in the crypto world. Contact: [email protected]  You can reach them via email at [email protected] OR Call/Text Number +1 (336)390-6684 his contact website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 23.10.25 21:43 patricialovick86

    How To Recover Your Bitcoin Without Falling Victim To Scams: A  Testimony Experience With Capital Crypto Recover Services, Contact Telegram: @Capitalcryptorecover Dear Everyone, I would like to take a moment to share my positive experience with Capital Crypto Recover Services. Initially, I was unsure if it would be possible to recover my stolen bitcoins. However, with their expertise and professionalism, I was able to fully recover my funds. Unfortunately, many individuals fall victim to scams in the cryptocurrency space, especially those involving fraudulent investment platforms. However, I advise caution, as not all recovery services are legitimate. I personally lost $273,000 worth of Bitcoin from my Binance account due to a deceptive platform. If you have suffered a similar loss, you may be considering crypto recovery, The Capital Crypto Recover is the most knowledgeable and effective Capital Crypto Recovery Services assisted me in recovering my stolen funds within 24 hours, after getting access to my wallet. Their service was not only prompt but also highly professional and effective, and many recovery services may not be trustworthy. Therefore, I highly recommend Capital Crypto Recover to you. i do always research and see reviews about their service, For assistance finding your misplaced cryptocurrency, get in touch with them, They do their jobs quickly and excellently, Stay safe and vigilant in the crypto world. Contact: [email protected]  You can reach them via email at [email protected] OR Call/Text Number +1 (336)390-6684 his contact website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 24.10.25 06:08 MATT PHILLIP

    I never imagined I’d fall for a crypto romance scam but it happened. Over the course of a few months, I sent nearly $150,000 worth of Bitcoin to someone I genuinely believed I was building a future with. When they disappeared without a trace, I was left heartbroken, humiliated, and financially devastated. For a long time, I didn’t tell anyone. I felt ashamed. But eventually, while searching for answers, I came across a Reddit thread that mentioned Agent Jasmine Lopez. I reached out, not expecting much. To my surprise, she treated me with kindness, not judgment. She used advanced tools like blockchain forensics, IP tracing, and smart contract analysis and with persistence and legal support, she was able to recover nearly 85% of what I lost. I know not everyone gets that kind of outcome, but thanks to [email protected] WhatsApp at +44 736-644-5035, I’ve started to reclaim not just my assets, but my confidence and peace of mind. If you’re going through something similar, you’re not alone and there is hope.

  • 24.10.25 06:40 elizabethrush89

    God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover Via Contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 24.10.25 06:40 elizabethrush89

    God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover Via Contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 24.10.25 06:54 MATT PHILLIP

    I never imagined I’d fall for a crypto romance scam but it happened. Over the course of a few months, I sent nearly $150,000 worth of Bitcoin to someone I genuinely believed I was building a future with. When they disappeared without a trace, I was left heartbroken, humiliated, and financially devastated. For a long time, I didn’t tell anyone. I felt ashamed. But eventually, while searching for answers, I came across a Reddit thread that mentioned Agent Jasmine Lopez. I reached out, not expecting much. To my surprise, she treated me with kindness, not judgment. She used advanced tools like blockchain forensics, IP tracing, and smart contract analysis and with persistence and legal support, she was able to recover nearly 85% of what I lost. I know not everyone gets that kind of outcome, but thanks to [email protected] WhatsApp at +44 736-644-5035, I’ve started to reclaim not just my assets, but my confidence and peace of mind. If you’re going through something similar, you’re not alone and there is hope.

  • 24.10.25 18:18 patricialovick86

    How To Recover Your Bitcoin Without Falling Victim To Scams: A  Testimony Experience With Capital Crypto Recover Services, Contact Telegram: @Capitalcryptorecover Dear Everyone, I would like to take a moment to share my positive experience with Capital Crypto Recover Services. Initially, I was unsure if it would be possible to recover my stolen bitcoins. However, with their expertise and professionalism, I was able to fully recover my funds. Unfortunately, many individuals fall victim to scams in the cryptocurrency space, especially those involving fraudulent investment platforms. However, I advise caution, as not all recovery services are legitimate. I personally lost $273,000 worth of Bitcoin from my Binance account due to a deceptive platform. If you have suffered a similar loss, you may be considering crypto recovery, The Capital Crypto Recover is the most knowledgeable and effective Capital Crypto Recovery Services assisted me in recovering my stolen funds within 24 hours, after getting access to my wallet. Their service was not only prompt but also highly professional and effective, and many recovery services may not be trustworthy. Therefore, I highly recommend Capital Crypto Recover to you. i do always research and see reviews about their service, For assistance finding your misplaced cryptocurrency, get in touch with them, They do their jobs quickly and excellently, Stay safe and vigilant in the crypto world. Contact: [email protected]  You can reach them via email at [email protected] OR Call/Text Number +1 (336)390-6684 his contact website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 24.10.25 18:18 patricialovick86

    How To Recover Your Bitcoin Without Falling Victim To Scams: A  Testimony Experience With Capital Crypto Recover Services, Contact Telegram: @Capitalcryptorecover Dear Everyone, I would like to take a moment to share my positive experience with Capital Crypto Recover Services. Initially, I was unsure if it would be possible to recover my stolen bitcoins. However, with their expertise and professionalism, I was able to fully recover my funds. Unfortunately, many individuals fall victim to scams in the cryptocurrency space, especially those involving fraudulent investment platforms. However, I advise caution, as not all recovery services are legitimate. I personally lost $273,000 worth of Bitcoin from my Binance account due to a deceptive platform. If you have suffered a similar loss, you may be considering crypto recovery, The Capital Crypto Recover is the most knowledgeable and effective Capital Crypto Recovery Services assisted me in recovering my stolen funds within 24 hours, after getting access to my wallet. Their service was not only prompt but also highly professional and effective, and many recovery services may not be trustworthy. Therefore, I highly recommend Capital Crypto Recover to you. i do always research and see reviews about their service, For assistance finding your misplaced cryptocurrency, get in touch with them, They do their jobs quickly and excellently, Stay safe and vigilant in the crypto world. Contact: [email protected]  You can reach them via email at [email protected] OR Call/Text Number +1 (336)390-6684 his contact website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 25.10.25 00:49 tyleradams

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  • 25.10.25 00:50 stevekalfman

    If you ever need hacking services, look no further. I found myself in a difficult situation after losing almost $510,000 USD in bitcoin. I was distraught and had no hope of survival because i lost my life savings to this scam, I had no chance of recovering my investment. Until i came across an article on google about ([email protected]). A real-life recovery expert, everything changed completely after contacting him and explaining my ordeal to him and he quickly stepped in and assisted me in recovering 95% of my lost funds. They guarantee their clients and i got the highest level of happiness their services are highly recommended. so I’m putting this here for anyone who require their services too" Email: [email protected]

  • 25.10.25 05:05 victoriabenny463

    A few months ago, I fell for what looked like a legitimate online trading platform. The website was sleek, the support team was responsive, and they even showed me fake profit charts that seemed to grow daily. I started small, and after a few test withdrawals worked, I invested more eventually depositing 2 Bitcoin in hopes of long-term returns. But one morning, when I tried to withdraw, everything changed. The platform suddenly locked my account, claiming there were additional fees to release my funds. The support chat stopped responding, and the website started giving error messages. That’s when I realized I’d been scammed. I was devastated. Two Bitcoins wasn’t pocket change, it was my savings. I filed reports online, but everyone told me it was impossible to recover crypto once it’s sent. Then, through a discussion forum, I came across Dexdert Net Recovery, a team specializing in tracing and recovering stolen digital assets. Skeptical but desperate, I reached out. Their response was immediate and professional. They asked for transaction IDs, wallet addresses, screenshots of my correspondence with the fake platform, and any proof of payment I had. Within days, their analysts traced the stolen Bitcoin through multiple wallets using blockchain forensics, They updated me step-by-step, Working with their recovery experts and blockchain partners, Dexdert Net Recovery successfully froze the funds and verified ownership of my wallet. After 2 days of persistence and verification, I finally saw my 2 Bitcoin restored back into my own wallet. I couldn’t believe it. What stood out most wasn’t just that they recovered my funds, but how transparent and supportive the Dexdert team was throughout the process. They educated me on crypto safety, how to spot fake trading sites, and how to secure my digital assets in the future. Dexdert Net Recovery truly lives up to its name. They gave me back not just my Bitcoin, but my peace of mind. Reach Out Information Below Via: Email: ([email protected]) Telegram: (https://t.me/Dexdertprorecovery) WhatsApp: (+1 (859) 609‑4156)

  • 25.10.25 10:13 wendytaylor015

    My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 25.10.25 10:13 wendytaylor015

    My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 26.10.25 01:03 Christopherbelle

    A terrible financial shock hit me hard. I lost $860,000 in a fake crypto scheme. Things looked good until I tried to cash out my earnings. Suddenly, my account vanished into thin air. I told the police many times, but help never showed up. Despair washed over me; I felt totally beaten. Then, I found Sylvester Bryant Intelligence. Right away, they were skilled and honest about the whole thing. They looked deep into my situation. They tracked where the stolen funds went. They fought hard for me every step of the way. To my great surprise, they got my money back. I thought that was impossible. I owe them so much for their hard work and truthfulness. Sylvester Bryant Intelligence restored my peace. If scams took your crypto, contact them now. Contact Info: Yt7cracker@gmail . com WhatsApp: ‪+1 512 577 7957. or +44 7428 662701.

  • 26.10.25 18:09 victoriabenny463

    A few months ago, I fell for what looked like a legitimate online trading platform. The website was sleek, the support team was responsive, and they even showed me fake profit charts that seemed to grow daily. I started small, and after a few test withdrawals worked, I invested more eventually depositing 2 Bitcoin in hopes of long-term returns. But one morning, when I tried to withdraw, everything changed. The platform suddenly locked my account, claiming there were additional fees to release my funds. The support chat stopped responding, and the website started giving error messages. That’s when I realized I’d been scammed. I was devastated. Two Bitcoins wasn’t pocket change, it was my savings. I filed reports online, but everyone told me it was impossible to recover crypto once it’s sent. Then, through a discussion forum, I came across Dexdert Net Recovery, a team specializing in tracing and recovering stolen digital assets. Skeptical but desperate, I reached out. Their response was immediate and professional. They asked for transaction IDs, wallet addresses, screenshots of my correspondence with the fake platform, and any proof of payment I had. Within days, their analysts traced the stolen Bitcoin through multiple wallets using blockchain forensics, They updated me step-by-step, Working with their recovery experts and blockchain partners, Dexdert Net Recovery successfully froze the funds and verified ownership of my wallet. After 2 days of persistence and verification, I finally saw my 2 Bitcoin restored back into my own wallet. I couldn’t believe it. What stood out most wasn’t just that they recovered my funds, but how transparent and supportive the Dexdert team was throughout the process. They educated me on crypto safety, how to spot fake trading sites, and how to secure my digital assets in the future. Dexdert Net Recovery truly lives up to its name. They gave me back not just my Bitcoin, but my peace of mind. Reach Out Information Below Via: Email: ([email protected]) Telegram: (https://t.me/Dexdertprorecovery) WhatsApp: (+1 (859) 609‑4156)

  • 27.10.25 11:15 harristhomas7376

    "In the crypto world, this is great news I want to share. Last year, I fell victim to a scam disguised as a safe investment option. I have invested in crypto trading platforms for about 10yrs thinking I was ensuring myself a retirement income, only to find that all my assets were either frozen, I believed my assets were secure — until I discovered that my BTC funds had been frozen and withdrawals were impossible. It was a devastating moment when I realized I had been scammed, and I thought my Bitcoin was gone forever, Everything changed when a close friend recommended the Capital Crypto Recover Service. Their professionalism, expertise, and dedication enabled me to recover my lost Bitcoin funds back — more than €560.000 DEM to my BTC wallet. What once felt impossible became a reality thanks to their support. If you have lost Bitcoin through scams, hacking, failed withdrawals, or similar challenges, don’t lose hope. I strongly recommend Capital Crypto Recover Service to anyone seeking a reliable and effective solution for recovering any wallet assets. They have a proven track record of successful reputation in recovering lost password assets for their clients and can help you navigate the process of recovering your funds. Don’t let scammers get away with your hard-earned money – contact Email: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 27.10.25 11:15 harristhomas7376

    "In the crypto world, this is great news I want to share. Last year, I fell victim to a scam disguised as a safe investment option. I have invested in crypto trading platforms for about 10yrs thinking I was ensuring myself a retirement income, only to find that all my assets were either frozen, I believed my assets were secure — until I discovered that my BTC funds had been frozen and withdrawals were impossible. It was a devastating moment when I realized I had been scammed, and I thought my Bitcoin was gone forever, Everything changed when a close friend recommended the Capital Crypto Recover Service. Their professionalism, expertise, and dedication enabled me to recover my lost Bitcoin funds back — more than €560.000 DEM to my BTC wallet. What once felt impossible became a reality thanks to their support. If you have lost Bitcoin through scams, hacking, failed withdrawals, or similar challenges, don’t lose hope. I strongly recommend Capital Crypto Recover Service to anyone seeking a reliable and effective solution for recovering any wallet assets. They have a proven track record of successful reputation in recovering lost password assets for their clients and can help you navigate the process of recovering your funds. Don’t let scammers get away with your hard-earned money – contact Email: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 27.10.25 17:08 raymondgonzales

    Three Cheers for Wizard Hilton Cyber Tech, Bitcoin Savior Extraordinaire In the ever-evolving world of cryptocurrency, where volatility and uncertainty reign supreme, one individual has emerged as a beacon of hope and innovation - Wizard Hilton Cyber Tech, the self-proclaimed "Bitcoin Savior Extraordinaire." This enigmatic figure, with his uncanny ability to navigate the complexities of the digital asset landscape, has captivated the attention of crypto enthusiasts and skeptics alike. Wizard Hilton Cyber Tech journey began as a humble programmer, tinkering with the underlying blockchain technology that powers Bitcoin. But it was his visionary approach and unwavering commitment to the cryptocurrency's potential that propelled him into the limelight. Through a series of strategic investments, groundbreaking algorithmic trading strategies, and a knack for anticipating market shifts, Wizard Hilton Cyber Tech has managed to consistently outperform even the savviest of Wall Street traders. Wizard Hilton Cyber Tech ability to turn even the most tumultuous of Bitcoin price swings into opportunities for substantial gains has earned him the moniker "Wizard," a testament to his unparalleled mastery of the digital currency realm. But Wizard Hilton Cyber Tech impact extends far beyond personal wealth accumulation - Wizard Hilton Cyber Tech has tirelessly advocated for the widespread adoption of Bitcoin, working tirelessly to educate the public, lobby policymakers, and collaborate with industry leaders to overcome the barriers that have long hindered the cryptocurrency's mainstream acceptance. With infectious enthusiasm and boundless energy, Wizard Hilton Cyber Tech has become a true champion of the Bitcoin cause, inspiring a new generation of crypto enthusiasts to embrace the transformative power of this revolutionary technology. As the digital currency landscape continues to evolve, Wizard Hilton Cyber Tech name will undoubtedly be etched in the annals of cryptocurrency history as a visionary, a trailblazer, and, above all, the Bitcoin Savior Extraordinaire. To get your stolen bitcoin back, reach out to Wizard Hilton Cyber Tech via: Email : wizardhiltoncybertech ( @ ) gmail (. ) com WhatsApp number  +18737715701 Good Day.

  • 27.10.25 17:20 fatimanorth

    The Federal Trade Commission said that more than $1 billion had been lost to cryptocurrency scams in 2023. Victims frequently lose everything, including hope, trust, and wealth. When your hard-earned money disappears into digital shadows, you feel trapped. Nowadays, cryptocurrency frauds are very common. You can get help from recovery specialist Marie at [email protected] and via WhatsApp at +1 7127594675.

  • 28.10.25 00:55 elizabethrush89

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  • 28.10.25 00:55 elizabethrush89

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  • 29.10.25 03:43 Christopherbelle

    A sudden money crisis struck me. I dropped $82,000 to a phony crypto scam. All seemed fine until I went to pull out my gains. Then, i was unable to get back my hard earned money. I reported it to the police several times. No aid came my way. Deep sadness hit me; I felt crushed. That's when I learned about Sylvester Bryant Intelligence. They acted quick and fair from the start. They checked my case closely. They followed the path of my lost cash. They pushed strong for me at each turn. In shock, they brought my funds back. I had figured it could not happen. I thank them for their effort and honesty. Sylvester Bryant Intelligence gave me calm again. If a scam stole your crypto, reach out to them today. Contact Info: Yt7cracker@gmail . com WhatsApp: +1 512 577 7957 or +44 7428 662701.

  • 29.10.25 10:56 wendytaylor015

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  • 29.10.25 10:56 wendytaylor015

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  • 30.10.25 09:49 Christopherbelle

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  • 30.10.25 12:03 elizabethrush89

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  • 31.10.25 13:25 Lillian Lizzy

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  • 31.10.25 13:25 Lillian Lizzy

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  • 01.11.25 03:27 elizabethrush89

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  • 01.11.25 03:27 elizabethrush89

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  • 01.11.25 15:47 kattygates

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  • 01.11.25 15:49 kattygates

    I met an individual on an international dating app, Bumpy. After talking for a few months, the individual encouraged me to start investing on crypto asset trading platform, btc01.org. I started trading and believed I was making profit until I tried to withdraw some of my money, I was asked to pay extra for tax which I did and they kept asking then I knew I have been scammed, I had to contact HACKWEST AT WRITEME DOT COM who then helped to recover the money, the total money I invest is $198,000 in bitcoin. The website is no longer operational. If anyone is in a similar issue, you can as well contact HACK WEST. They also fixed my credit report.

  • 02.11.25 10:55 Christopherbelle

    I suffered a crushing blow when $45,000 slipped away in a phony crypto scam. It all looked great at first. But when I went to pull out my gains, my account just vanished. I called the cops over and over. Still, no luck. I felt shattered and lost. That’s when I stumbled on Sylvester Bryant Intelligence. Things turned around fast. Right away, they showed real openness, sharp skills, and a drive to fix it. They tracked my missing money step by step. And they pushed hard until they got it back. I honestly didn’t believe it could happen. Their straight-up approach and solid work brought back my calm. If a scam took your crypto, reach out to them now. yt7cracker@gmail . com | WhatsApp: +1 512 577 7957 or +44 7428 662701

  • 02.11.25 10:56 Christopherbelle

    I suffered a crushing blow when $45,000 slipped away in a phony crypto scam. It all looked great at first. But when I went to pull out my gains, my account just vanished. I called the cops over and over. Still, no luck. I felt shattered and lost. That’s when I stumbled on Sylvester Bryant Intelligence. Things turned around fast. Right away, they showed real openness, sharp skills, and a drive to fix it. They tracked my missing money step by step. And they pushed hard until they got it back. I honestly didn’t believe it could happen. Their straight-up approach and solid work brought back my calm. If a scam took your crypto, reach out to them now. yt7cracker@gmail . com | WhatsApp: +1 512 577 7957 or +44 7428 662701

  • 02.11.25 15:23 michaeldavenport238

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  • 02.11.25 15:23 michaeldavenport238

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  • 04.11.25 04:59 Christopherbelle

    How to Recover Bitcoin Stolen by a Scammer I dropped £75,000 into a fake crypto scheme. Everything seemed perfect right from the start. But when I tried to cash out my profits, the whole account disappeared. I rang the police time and again. They offered no help at all. I felt broken and alone. Then I found Sylvester Bryant Intelligence. My luck changed in no time. They spoke plainly, worked smart, and focused on my case. They followed the trail of my lost cash bit by bit. They fought until they recovered it all. I never thought it was possible. Their honest approach and expertise restored my peace. If a scam has stolen your crypto, contact them now. [email protected] | WhatsApp: +1 512 577 7957 or +44 7428 662701

  • 04.11.25 09:30 robertalfred175

    CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: 📧 Email: [email protected] 📱 Telegram: @Capitalcryptorecover Contact: [email protected] 📞 Call/Text: +1 (336) 390-6684 🌐 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 04.11.25 09:30 robertalfred175

    CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: 📧 Email: [email protected] 📱 Telegram: @Capitalcryptorecover Contact: [email protected] 📞 Call/Text: +1 (336) 390-6684 🌐 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 05.11.25 02:43 jordan_11

    I made a mistake of not researching about their their investment firm(Binary option), it had a lot of promises which made me fall for all their fake promises , after trying to get my withdrawal out from there, I started having a lot of difficulties. Then I contacted their customer support, they only replied a week after and strangely wanted me to make more deposits just to enable my withdrawal, so i started my research of how I could report this treacherous company to the necessary authorities and also maybe i could get back my investment, The only people that were willing to help me out was Treqora Intel, their customer support replied so fast and immediately directed me to their investigative team which took my up my case and started the tracing and reclaim process with swift, after a week i got an email from Treqora Intel stating that a partial amount had been reclaimed, I was so grateful about their help , then I was asked to decide if I wanted a Partial deposit or wanted all my investment reclaimed and sent to me at once, But I was so desperate at the time so I asked that my partial reclaimed ETH be sent to me first , So the deposit took about few minutes before i got it in my wallet and withdrew it. Then my remaining investment took 2 weeks to get back according to their customer support at Treqora Intel. Immediately They got it, I was contacted again Via email that my reclaimed had been fully reclaimed, so grateful till this day to Treqora Intel for taking their time to help me out with what could have been a very depressing moment to me. And yes no upfront payment until the reclaim has been completed and you've been paid fully. Email:support@treqora. com 📱 WhatsApp: ‪‪‪+1 (7 7 3) 9 7 7 - 7 8 7 7‬ ‬‬ 🌐 Website: Treqora. com.

  • 05.11.25 02:44 jordan_11

    Crypto Recovery Services _Hire Treqora Intel

  • 05.11.25 02:48 jordan_11

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  • 05.11.25 16:20 robertalfred175

    CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: 📧 Email: [email protected] 📱 Telegram: @Capitalcryptorecover Contact: [email protected] 📞 Call/Text: +1 (336) 390-6684 🌐 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 05.11.25 16:21 robertalfred175

    CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: 📧 Email: [email protected] 📱 Telegram: @Capitalcryptorecover Contact: [email protected] 📞 Call/Text: +1 (336) 390-6684 🌐 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 07.11.25 02:26 MATT PHILLIP

    I never imagined I’d fall for a crypto romance scam but it happened. Over the course of a few months, I sent nearly $184,000 worth of Bitcoin to someone I genuinely believed I was building a future with. When they disappeared without a trace, I was left heartbroken, humiliated, and financially devastated. For a long time, I didn’t tell anyone. I felt ashamed. But eventually, while searching for answers, I came across a Reddit thread that mentioned Agent Jasmine Lopez a crypto recovery agent. I reached out, not expecting much. To my surprise, she treated me with kindness, not judgment. She used advanced tools like blockchain forensics, IP tracing, and smart contract analysis and with persistence and legal support, she was able to recover nearly 85% of what I lost. I know not everyone gets that kind of outcome, but thanks to [email protected] WhatsApp at +44 736-644-5035, I’ve started to reclaim not just my assets, but my confidence and peace of mind. If you’re going through something similar, you’re not alone and there is hope.

  • 07.11.25 09:33 Christopherbelle

    How to Recover Bitcoin Stolen by a Scammer I dropped £75,000 into a fake crypto scheme. Everything seemed perfect right from the start. But when I tried to cash out my profits, the whole account disappeared. I rang the police time and again. They offered no help at all. I felt broken and alone. Then I found Sylvester Bryant Intelligence. My luck changed in no time. They spoke plainly, worked smart, and focused on my case. They followed the trail of my lost cash bit by bit. They fought until they recovered it all. I never thought it was possible. Their honest approach and expertise restored my peace. If a scam has stolen your crypto, contact them now. yt7cracker@gmail. com | WhatsApp: +1 512 577 7957 or +44 7428 662701

  • 07.11.25 16:05 MATT PHILLIP

    I never imagined I’d fall for a crypto romance scam but it happened. Over the course of a few months, I sent nearly $184,000 worth of Bitcoin to someone I genuinely believed I was building a future with. When they disappeared without a trace, I was left heartbroken, humiliated, and financially devastated. For a long time, I didn’t tell anyone. I felt ashamed. But eventually, while searching for answers, I came across a Reddit thread that mentioned Agent Jasmine Lopez a crypto recovery agent. I reached out, not expecting much. To my surprise, she treated me with kindness, not judgment. She used advanced tools like blockchain forensics, IP tracing, and smart contract analysis and with persistence and legal support, she was able to recover nearly 85% of what I lost. I know not everyone gets that kind of outcome, but thanks to [email protected] WhatsApp at +44 736-644-5035, I’ve started to reclaim not just my assets, but my confidence and peace of mind. If you’re going through something similar, you’re not alone and there is hope.

  • 07.11.25 23:15 Christopherbelle

    How to Recover Bitcoin Stolen by a Scammer; I dropped £75,000 into a fake crypto scheme. Everything seemed perfect right from the start. But when I tried to cash out my profits, the whole account disappeared. I rang the police time and again. They offered no help at all. I felt broken and alone. Then I found Sylvester Bryant Intelligence. My luck changed in no time. They spoke plainly, worked smart, and focused on my case. They followed the trail of my lost cash bit by bit. They fought until they recovered it all. I never thought it was possible. Their honest approach and expertise restored my peace. If a scam has stolen your crypto, contact them now. yt7cracker@gmail. com | WhatsApp: +1 512 577 7957 or +44 7428 662701

  • 07.11.25 23:30 harristhomas7376

    "In the crypto world, this is great news I want to share. Last year, I fell victim to a scam disguised as a safe investment option. I have invested in crypto trading platforms for about 10yrs thinking I was ensuring myself a retirement income, only to find that all my assets were either frozen, I believed my assets were secure — until I discovered that my BTC funds had been frozen and withdrawals were impossible. It was a devastating moment when I realized I had been scammed, and I thought my Bitcoin was gone forever, Everything changed when a close friend recommended the Capital Crypto Recover Service. Their professionalism, expertise, and dedication enabled me to recover my lost Bitcoin funds back — more than €560.000 DEM to my BTC wallet. What once felt impossible became a reality thanks to their support. If you have lost Bitcoin through scams, hacking, failed withdrawals, or similar challenges, don’t lose hope. I strongly recommend Capital Crypto Recover Service to anyone seeking a reliable and effective solution for recovering any wallet assets. They have a proven track record of successful reputation in recovering lost password assets for their clients and can help you navigate the process of recovering your funds. Don’t let scammers get away with your hard-earned money – contact Email: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 07.11.25 23:30 harristhomas7376

    "In the crypto world, this is great news I want to share. Last year, I fell victim to a scam disguised as a safe investment option. I have invested in crypto trading platforms for about 10yrs thinking I was ensuring myself a retirement income, only to find that all my assets were either frozen, I believed my assets were secure — until I discovered that my BTC funds had been frozen and withdrawals were impossible. It was a devastating moment when I realized I had been scammed, and I thought my Bitcoin was gone forever, Everything changed when a close friend recommended the Capital Crypto Recover Service. Their professionalism, expertise, and dedication enabled me to recover my lost Bitcoin funds back — more than €560.000 DEM to my BTC wallet. What once felt impossible became a reality thanks to their support. If you have lost Bitcoin through scams, hacking, failed withdrawals, or similar challenges, don’t lose hope. I strongly recommend Capital Crypto Recover Service to anyone seeking a reliable and effective solution for recovering any wallet assets. They have a proven track record of successful reputation in recovering lost password assets for their clients and can help you navigate the process of recovering your funds. Don’t let scammers get away with your hard-earned money – contact Email: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 07.11.25 23:32 Christopherbelle

    How to Recover Bitcoin Stolen by a Scammer; I dropped £75,000 into a fake crypto scheme. Everything seemed perfect right from the start. But when I tried to cash out my profits, the whole account disappeared. I rang the police time and again. They offered no help at all. I felt broken and alone. Then I found Sylvester Bryant Intelligence. My luck changed in no time. They spoke plainly, worked smart, and focused on my case. They followed the trail of my lost cash bit by bit. They fought until they recovered it all. I never thought it was possible. Their honest approach and expertise restored my peace. If a scam has stolen your crypto, contact them now. yt7cracker@gmail. com | WhatsApp: +1 512 577 7957 or +44 7428 662701

  • 07.11.25 23:34 Christopherbelle

    How to Recover Bitcoin Stolen by a Scammer; I dropped £75,000 into a fake crypto scheme. Everything seemed perfect right from the start. But when I tried to cash out my profits, the whole account disappeared. I rang the police time and again. They offered no help at all. I felt broken and alone. Then I found Sylvester Bryant Intelligence. My luck changed in no time. They spoke plainly, worked smart, and focused on my case. They followed the trail of my lost cash bit by bit. They fought until they recovered it all. I never thought it was possible. Their honest approach and expertise restored my peace. If a scam has stolen your crypto, contact them now. yt7cracker@gmail. com | WhatsApp: +1 512 577 7957 or +44 7428 662701

  • 09.11.25 03:29 wendytaylor015

    My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 09.11.25 03:29 wendytaylor015

    My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 05:06 Christopherbelle

    I lost $52,000 in USDT to a scam. That hit me hard. USDT is a stable cryptocurrency tied to the US dollar. It keeps its value steady. I thought I had found a sure way to grow my money. Things looked good at first. I even built up profits to $120,000. But when I went to pull out my earnings, the platform blocked me. No access. No funds. Panic set in. I felt trapped and helpless. Scams like this target crypto users all the time. They promise quick gains. Then they vanish with your money. Each year, people lose billions to these tricks. I searched for help everywhere. Forums, support groups. Nothing worked. That's when a friend stepped in. He had faced a similar mess before. He told me about Sylvester Bryant. My friend swore by his skills. So I reached out right away. His email is [email protected]. Sylvester Bryant turned it all around. He listened to my story without judgment. His team got to work fast. They started by reviewing every detail of the scam. Step by step, they traced the path of my stolen USDT. They used tools to follow the blockchain. That's the public record of crypto transactions. It shows where funds move. But scammers hide their tracks. Bryant's group dug deep. They contacted exchanges and networks involved. Day after day, they pushed forward. No shortcuts. They kept me updated the whole time. Every email, every call was clear and honest. In the end, they recovered my full amount. That $52,000 came back to me. The process took focus and grit. Bryant's honesty stood out. He charged no hidden fees. Just straight work for results. My stress melted away. I could breathe again. Sleep came easier. My trust in recovery options grew. If a scam has taken your money, act now. Reach out to Sylvester Bryant. He handles cases like this with care. Email him at [email protected]. Or on WhatsApp at +1 512 577 7957 or +44 7428 662701. Don't wait. Get your funds back.

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